Bill's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 5 adult tickets and 14 student tickets for a total of $198. The school took in $156 on the second day by selling 10 adult tickets and 8 student tickets. Find the price of an adult ticket and the price of a student ticket.

The price of an adult ticket = $6

The price of a student ticket = $12

Step-by-step explanation:

Let the price of an adult ticket be a

Let the price of a student ticket be b.

From the question,

5a + 14b = 198 equation i

10a + 8b = 156 equation ii

Multiply equation i by 10

Multiply equation ii by 5

50a + 140b = 1980 equation iii

50a + 40b = 780 equation iv

Subtract iv from iii

100b = 1200

b = 1200/100

b = 12

Put the value of b into equation ii

10a + 8b = 156

10a + 8(12) = 156

10a + 96 = 156

10a = 156-96

10a = 60

a = 6

The price of an adult ticket = $6

The price of a student ticket = $12

.there can be infinite values of m and n that can satisfy the above equation. for each value of m of m or n. there maybe infinite sets of solution for the above

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is